A moment problem for discrete nonpositive measures on a finite interval

This article has been made available through the Brunel Open Access Publishing Fund.We will estimate the upper and the lower bounds of the integral ∫01Ω(t)dμ(t), where μ runs over all discrete measures, positive on some cones of generalized convex functions, and satisfying certain moment conditions with respect to a given Chebyshev system. Then we apply these estimations to find the error of optimal shape-preserving interpolation

Deformed Supersymmetric Mechanics

Motivated by a recent interest in curved rigid supersymmetries, we construct a new type of N=4, d=1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry is a deformation of the standard N=4, d=1 supersymmetry by a mass parameter m. As instructive examples we consider, at the classical and quantum levels, the models associated with the supermultiplets (1,4,3) and (2,4,2) and find out interesting interrelations with some previous works on non-standard d=1 supersymmetry. In particular, the d=1 systems with "weak supersymmetry" are naturally reproduced within our SU(2|1) superfield approach as a subclass of the (1,4,3) models. A generalization to the N=8, d=1 case implies the supergroup SU(2|2) as the candidate deformed worldline supersymmetry.Comment: 1 + 36 pages, Substantial revision: new comments, footnotes, references and Appendix B added, typos corrected; published versio

Nuclear effects and higher twists in F3 structure function

We analyze the CCFR collaboration iron target data on the xF3 structure function making particular emphasis on the extraction of the higher twist contributions from data. Corrections for nuclear effects are applied in order to extract data on the structure function of the isoscalar nucleon. Our analysis confirms the observation made earlier, that the higher twist terms depend strongly on the level to which QCD perturbation theory analysis is applied. We discuss the impact of nuclear effects on the higher twist term as well as on the QCD scale parameter Lambda_{\bar{MS}} extracted from the fit to data.Comment: 16 pages, 2 figure

Supercritical holes for the doubling map

For a map $S:X\to X$ and an open connected set ($=$ a hole) $H\subset X$ we define $\mathcal J_H(S)$ to be the set of points in $X$ whose $S$-orbit avoids $H$. We say that a hole $H_0$ is supercritical if (i) for any hole $H$ such that $\bar{H_0}\subset H$ the set $\mathcal J_H(S)$ is either empty or contains only fixed points of $S$; (ii) for any hole $H$ such that \barH\subset H_0 the Hausdorff dimension of $\mathcal J_H(S)$ is positive. The purpose of this note to completely characterize all supercritical holes for the doubling map $Tx=2x\bmod1$.Comment: This is a new version, where a full characterization of supercritical holes for the doubling map is obtaine